Abstract
What is in this chapter? Let X n be the state of a Markov chain at time n. Assume that X0, the initial state of the chain, is distributed according to a distribution π. That is, assume that the probability that X0 is in state i is π(i). Can we find a distribution π such that if X0 has distribution π then X n , for all times n, also has distribution π? Such a distribution is said to be stationary for the chain. This chapter deals with the existence of and the convergence to stationary distributions.
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Notes and references
In this chapter we have followed the treatment of Durrett (1996). If the chain is periodic it is still possible to get some convergence results (see Durrett (1996)).
For more on the physics on the Ehrenfest chain as well as some very interesting computations see Bhattacharya and Waymire (1990) (Chapter III, Section 5).
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© 1999 Springer Science+Business Media New York
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Schinazi, R.B. (1999). Stationary Distributions of a Markov Chain. In: Classical and Spatial Stochastic Processes. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1582-0_2
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DOI: https://doi.org/10.1007/978-1-4612-1582-0_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7203-8
Online ISBN: 978-1-4612-1582-0
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